Yes, you are correct, the above language is not LL(2) as I thought,
because both forms of recursion can pile up an indefinitely long
string of b characters before the central "a c" string, the language
cannot be parsed with an LL(k) grammar, becuase you cannot tell
strictly from the prefix what kind of recursion you have.

Obviously, the construction of a language that is precisely LL(2) is
more subtle than I thought. I still know you need at least one
central recursion in the language (otherwise, if the language has only
left recursion or right recursion, it is regular), but how you get it
so that two tokens are required to decipher the recursion rather than
just one (without requiring unbounded numbers of tokens), is something
I clearly don't have an intuition for, and I don't have a parsing text
handy here.